GEOPHYSICALRN•EARCH LET]7ERS,VOL. 19, NO. 10, PAGES 1057-1060,MAY 22, 1992
STABILITYOF (Mg,Fe)SiO3
PEROVSKITE
AND TIlE STRUCTURE
OFTHE LOWERMOSTMANTLE
Lars Stixrude• and M. S. T. Bukowinski
Dept.of GeologyandGeophysics,
Universityof Califomiaat Berkeley
constituentoxidespermits a solid D", since oxides are
expectedto be more refractorythantheir compounds,and
provides
a possibleexplanationof the region'sdistinctive
pressure,
temperature
andcompositional
regime
oftheEarth's
manfie.The breakdownof perovskiteto its constituent
oxides
seismicproperties
[Stixrudeand Bukowinski,1990].
Here we showthat the breakdownof perovskiteto its
appears
unlikely,
evenundertheextreme
conditions
of the
constituent
oxidesis unlikelyin theEarth. The reactiondoes
core-mantle
boundary. This reactionhad beenproposedto
reconcile
estimates
of silicatemeltingwith seismicobservation occurat appropriate
pressure-temperature
conditions
butonly
for iron contentsso high that the productsdisagreeseverely
andproposed
geotherrns.
with the densityandbulk modulusof the lowermostmantle.
Introduction
We discussother possible resolutionsof the apparent
discrepancybetween the perovsldte melting curve, the
Abstract.
Thermodynamic analysis shows that
(Mg,Fe)SiO3
perovskite
is stablethroughout
the likely
The D" layer is a few hundredkilometer thick region of
anomalous
seismicpropertiesat the baseof the mantle. It is
distinguished
by stronglateral heterogeneity,small, often
geothermandseismicobservations.
Thermodynamic
Formalism
negative,seismic velocity gradients, and velocity
discontinuities
over muchof its upperboundary[Youngand
Lay,1987;WeberandKi•rnig, 1990]. The mineralogical
or
compositionalchanges responsible for these unusual
properties
remainunknown.
(Mg,Fe)SiO3perovskiteis generallyacceptedasthe most
Our resultsare basedon semi-empiricalthermodynamic
potentials[Stixrudeand Bukowinski,1990]. The Gibbsfree
energy, G, of a phaseconsistingof a solid solutionof N
species
asa functionof pressure,
P, andtemperature,
T, is:
N
abundantmineral in the lower mantle. Perovskite dominated
assemblages
readilyaccountfor the seismicpropertiesof the
bulkof thelower mantleandphaseequilibriumstudiesover
mostof themanfie'spressure-temperature
regimeconfirmits
stability
[KnittleandJeanloz,1987]. However,thestabilityof
perovskite
at pressure-temperature
conditions
characteristic
of
D"hasnotyet beenexperimentallyaddressed.
A comparisonof recentlyproposedgeotherms[Jeanloz,
1990]withsilicatemeltingcurvesin thedeepmantleindicates
thatperovskitecannotbe a constituentof D"[$tixrude and
Bukowinski,1990]. Near the core-mantleboundary,its
meltingpoint falls more than a thousanddegreesbelow
G(P,T) = i---1
•x•Gi(P,T) + RTxi lnai
(1)
wherexi, Gi andai are the mole fraction,Gibbs free energy
andactivityof species
i. The latteris approximated
by regular
solution theory.
We write the free energy as'
Gi(P,T)=Fi(V,T)+PVi,
where V is the molar volume and
assumethattheHelmholtzfree energy,Fi, canbe dividedinto
a referenceterm, a purely volume dependentpart given by
Birch-Murnaghan
finite straintheory,a thermalpart,givenby
Debyetheoryandanelectroniccontribution:
Fi(V,T ) = Fo + Fc(V, To)+[Fr,v(V,T)- Frn(V,To)]
estimated
temperatures
in theEarth.Theproposed
core-mantle
+[FEt.(V,T)- Fez(V, To)]
(2)
boundary
temperature
is primarilydetermined
by themeasured
whereFo is the valueat P=0 and T=To. The parametersare
melting
temperature
of ironundershock-loading
[Williamset
or constrained
by experimental
dataor
al.,1987]whichis foundto besignificantly
higherthanmodel eitherdirectlymeasured
(Table 1). Referencefreeenergies
calculations
of theironhugoniot
hadpredicted
[B•:own
and firstprinciplescalculations
and interaction parameters,W, are constrainedby phase
blcQueen,1982]. If the shockwave measurements
andthe
The remainingparameters,
including
predicted
perovskite
meltingcurveareapproximately
correct, equilibriameasurements.
Vo, the isothermalbulk modulus, Ko, and its pressure
theconstitution
of D" mustdiffersubstantially
fromtherestof
derivative,
Ko',theDebyetemperature,
0o,andits logarithmic
themanfie,since seismicobservationsrule out significant
volume
derivative,
7o,
are
determined
by inverting
amounts
of partialmelt. Assumingthat the region'sbulk
compression,
thermalexpansionand calorimetricdata. The
chemistry
is dominated,
like therestof themantle,by Mg, Fe
electronicterm appearsonly for the metallic high pressure
andSi oxide components,perovskitemust undergoa
transformation
to a highpressure
phaseor assemblage
under phaseof FeO andis givenby freeelectrontheory.
Eq. 2, oftenseenin the form of its volume derivative- the
D"conditions.
A proposed
breakdown
of perovskite
to its
1Nowat: Geophysical
Laboratory
andCenterfor High
Pressure
Research,
Carnegie
Institution
ofWashington
Copyright
1992bytheAmerican
Geophysical
Union.
Papernumber92GL01066
0094-8534/92/92GL-01066503.00
Mie-Grtineisenequationof state- describesa wide varietyof
thermodynamic
properties
of mantlemineralsat highpressures
and temperatures,
includingtheir equationsof state,phase
equilibriaandmeltingbehavior.To theextentthatartharmonic
termsarenegligible,thepotentials
remainsufficientlyaccurate
for our purposesat the extreme pressure-temperature
conditionsof interesthere. The cold part remains well
constrainedby experimentalmeasurementsfor most of the
1057
1058
Stixrude& Bukowinski:
Stabilityof Perovskite
in D"
TABLEi. Parameters
of thethermodynamic
potentials.
Globalparameter
set.Highandlowtemperature
parameters
are
identical
except:Fo of Mg-Sp(-98.0,-88.6),Fe-Sp(-97.6,-90.9),Mg-Pv(-0.4,6.6),Fe-Pv(45.5,35.2)andW of Sp
(3.6,4.1) andMw (13.5, 12.6). Parentheses
containestimated
uncertainties
in thelastdigits.
Phase
FormulaFo,kJ/mol Vo,cm3/molKo,GPa Ko'
0o,K
7o
W,kJ/mol
Spinel(Sp)
Mg2SiO4
-92.4
39.65
183(3)
4.1(5)
1017(10)
1.21(10)
2.8
Perovskite
(Pv)
Fe2SiO4
MgSiO3
FeSiO3
-94.1
3.4
40.5
42.02
24.46
25.49
192(3)
263(7)
263(7)
4.1(5)
3.9(5)
3.9(5)
781(10)
1017(10)
749(50)
1.21(10)
1.96(10)
1.96(10)
2.8
0
0
Magnesio-
MgO
0
11.25
160(2)
4.1(2)
776(10)
1.45(10)
13.1
w'dstite(Mw)
FeO
0
12.25
152(2)
4.9(2)
434(50)
1.45(10)
13.1
Magnesio-
MgO
139.7
10.79
161(10) 4.1(1.0)
698(50)
1.36(20)
13.1
wastitelI(Mw!!)
FeO
55.9
10.84
205(10)
6(1)
630(50)
1.45(20)
13.1
Stishovite
(St)
SiO2
0
14.01
314(8)
8.8(8)
1152(10)
1.35(10)
0
Properties
of PcII arefromBukowinski
[1985];thoseof Wu II fromJackson[1990]. q=2.5(1.7)for perovskite[Hemleyet
al., 1992]andis assumed
to be 1(2) for ali otherphases.Inversion
of experimental
datafor all otherparameters
will be
discussed
in a forthcoming
publication.
30
relevantphases,
whilethethermalpartcloselyapproaches
its
hightemperature
limitingbehavior(T/O> 4). In thislimit,
28
results are insensitive to the detailed form of the vibrational
densityof stateswhichis approximately
represented
in the
Debyemodel.Theadequacy
of theregularsolution
modeland
the assumedvolume dependenceof 7 is more difficult to
26
241
evaluate. We ensure that our results are insensitive to wide
variations in W and q, the secondlogarithmic volume
22
derivative of 0.
20
Results
18
Calculatedpseudobinary
orthosilicate
phaseequilibriaare
comparedwith the low and high temperature
experimental
16
resultsof Ito and Takahashi[1989] in Figure 1. By inverting
low andhightemperature
dataseparately
for thereference
free
energiesof the relevant species(Table 1), we obtained
excellent fits to the observations. However, it proved
impossibleto reproducebothexperiments
with a singlesetof
referencefreeenergies.Parameters
whichgivethebestglobal
fit reproduce the general topology but the calculated
coexistenceloopsshift towardsmoreiron rich compositions
with decreasingtemperaturewhile the reverseis observed
experimentally.The morecomplexthermodynamic
modelof
Fei et al. [1991] producesvery similar resultsand is also
unableto fit the data. The reasonfor this discrepancy
is
unclear. Barring severe deficienciesin two very different
thermodynamic
formulations,insufficientequilibrationor an
unquenchablephasetransitionin one or more of the relevant
speciesmay beresponsible.
Considering
the discrepancies
apparentin Figure1 to be an
additionalsourceof uncertainty,the resultingerrorsin our
calculated phase diagrams at D" pressure-temperature
conditions are small and will not affect our basic conclusions
(Figure 2). Differencesbetweenthe predictionsof high
temperatureand global parametersets are reduced by
increasingpressure.The stabilityfield of perovskiteis very
wide at pressuresgreater than 60 GPa (1500 km depth),
regardless
of theparameter
setusedin thecalculations;
thelow
temperature
parameters
produceanevenwiderstabilityfield of
perovskite.
The predicted high pressurephase diagrams satisfy
experimental
constraints,
includingthetransitionof wiistiteto
14
28
Pv+Mw
26•-
//'//
ß d' / /
,:2Mw+St]
24
•
22
20
1373 K
16
I
14
0.0
I
0.2
Mg2SiO4
I
0.4
.
I
0.6
XF½
I
0.8
1.0
FeaSiOn
Fig. 1. Pressure-composition
phase diagram at two
temperatures.
XFe=Fe/(Mg+Fe).Experimental
observations
of pseudo-unary,
-binary and -ternary coexistence
are
indicated by open and closed symbols and crosses,
respectively.
Thesolidlinesarecalculations
basedonhigh
andlowtemperature
parameter
sets.Dashed
linesarebased
onthebestfit globalparameter
set.
1059
Stixrude
& Bukowinski:
Stabilityof Perovskite
in D"
discovered
highpressure
form [Tsuchidaand Yagi, 1989]
140
i
-
120
80
positionof phaseboundarieson the diagram. Perhapsthe
largestuncertainty
lies in the pressure
of the assumed
phase
transitionin periclase.The first principlescalculations
of
Bukowinski[1985] providea probablelower boundon the
transition
pressure
of 205 GPa at 300 K, muchlowerthanthe
valueadopted
herefrommorerecentresults[500 GPa;Mehl et
al., 1988]. Adoptingthe lower valueexpandsthe Mw II+St
fieldsomewhat
butnotenoughto encompass
theEarth.
Discussion and Conclusions
60
0.0
have a much smaller effect on the location of the Earth and the
0.2
Mg2SiO,•
0.4
0.6
Xr½
0.8
1.0
Fe•SiO4
Our resultsindicatethat the breakdownof (Mg,Fe)SiO3
perovsldte
to its constituent
oxidesis unlikelyin the Earth. If
core-mantle
boundarytemperatures
aremuchlowerthanthose
derivedfrom shockwave experiments,severalalternative
explanations
for theseismicreflectorsat the baseof themantle
arepossible.Smallamountsof stishovitemaybe responsible,
from silica enrichmentrelative to metasilicatestoichiometry
Fig.2. Highpressure
Mg2SiO4-Fe2SiO4
phasediagram
at
3500K. Solidand dashedcurvesare calculatedwith the high
SiO2
St
temperature
andglobalparameter
setsrespectively.
]DENSITY
(Mg
rn
7 P=136
GPa
T=5000 K
a metallic form, observed near 70 GPa in diamond cell
[r•000 K] andshockwave [T--1000K] experiments[see
Jeanloz,1990] andperovskitesyntheses
up to 127 GPa and
approximately
2500 K [Knittle and Jeanloz,!987]. Our
resultsclosely resemblethe predictionsof Jeanloz and
Thompson
[1983] below 80 GPa. At higher pressures,our
calculations
show two pseudobinarycoexistenceloops,as
requked
bythephaserule,in placeof theirfour-phase
field.
The ternary MgO-FeO-SiO2 diagramsummarizesthe
important
results(Figure3). To obUdna conservative
estimate
of the stability of perovskitein D", we have chosenan
extreme
temperature
(5000 K) sincelowervalueswidenthe
perovskite
stabilityfield. Superimposed
onthephasediagram
arecontours
of densityandacousticvelocitycalculated
with
thesamethermodynamic
potentialformalismandthe same
parameters
used to determine the phase diagram. The
intersection
of the contourscorresponding
to the observed
density
andacousticvelocityat the baseof the manfie[e.g.
Dziewonskiand Anderson, 1981], which representthe
location
of the Earthat this pressure,
lies well withinthe
stability
fieldof perovskite.
Theuncertainties
in seismic
properties
nearthecoremantle
boundary
arelargerthanthosein therestof themantlebut
correspond
to an areaof thephasediagrammuchsmallerthan
EARTH
• 5.•"
//
MgO Mw
SiO2
MwII FeO
st
[K's
(GPa)
'
MgO Mw
Mwn FeO
Fig. 3. TernaryMgO-FeO-SiO2 phasediagramat 136 GPa
and5000K calculated
withthehightemperature
parameter
set.
Contoursof density(upperfigure)andadiabaticbulkmodulus
calculations
arealsomuchtoosmallto substantially
alterthe
(dottedlines). The shading,
phase
diagram.Variationsin experimentally
constrained (lowerfigure)aresuperimposed
shownonlyin theupperfigurefor clarity,indicatesthefield of
parameterswithin their uncertainties and in W's from 0 to
possibleintersections
of the contourscorresponding
to the
three
times
theirnominal
values
movethephase
boundaries
by
<0.4XFeunits.Forall parameters
butq of perovskite,
the observeddensity and adiabatic bulk modulus of the Earth
allowedby uncertainties
in calculated
andseismically
observed
changes
are<0.2. Extremevariationsin Fo•s,obtainedby
extrapolatingtheir apparent temperaturedependence densitiesandbulkmoduli. Adoptinga value of 205 GPa for
(difference
between
low-Tandhigh-T
parameter
sets)
to5000 the roomtemperaturephasetransitionin periclaseeliminates
Kalso
failstoexclude
theEarthfromtheperovskite
stability Mw fromthe diagramandshiftsthePv+Mw II+St coexistence
field.Alternative
values
of KoandKo'forperovskite
(246 field towardslower iron contents(XFe(Pv)=0.58,XFe(Mw
thatof theperovskite
stabilityfield. Uncertainties
in the
GPa,4.5)or thetransformation
of stishovite
to itsrecently
1060
Stixrude& Bukowinski:Stabilityof Perovskite
in D"
(Figure3). The phasetransitionof magnesiowtistite
to its
highpressure
formmayproduceanomalous
velocitygradients
nearthecore-mantleboundary,althoughit appears
muchtoo
diffuseto producea seismicdiscontinuity
(Figure2). Still
unobserved phase transitions in calcic, diopsidic or
(Mg,Fe)SiO3perovskite,
includingthepredicted
orthorhombic
to cubic transition in the latter, may producevelocity
discontinuities
at the appropriate
pressures
[seeHemleyand
Cohen, 1992]. Partial reactionof Mg-rich perovskitewith
ironalloys,similarto thatobserved
atlowerpressures
[Knittle
andJeanloz,1991],may alsoproduceseismicreflectors.
All of theseexplanationsrely on perovskitedominated
assemblages
and thus cannotreconcilegeothermsbasedon
shockwave experiments
with the lack of partialmelt in D".
The meltingpoint of iron undershockloadingandin static
compressionexperimentsat lower pressuresis currentlya
matter of active debate [Ross et al., 1990; Boehler et al.,
1990]. However, if the shockwave data and the predicted
perovskitemelting curve are approximatelycorrect,they
requireeitherthe absence
of Mg-richperovskite
fromD" or a
substantialchangein its properties,probablymuchgreater
thanthat associated
with the predictedorthorhombic
to cubic
phasetransformation. An exotic bulk compositionin D",
perhapsdominated
by Ca andA1oxidecomponents
[Ruffand
Anderson, 1980], may be required. Alternatively, a
breakdownor transformation
of (Mg,Fe)SiO3perovskiteto a
morediverseassemblage
thanthoseconsidered
hereremainsa
possibleexplanationof the seismicreflectorsandthe absence
of melt in D". Considerationof otherchemicalcomponents
may lower the free energyof the non-perovskite
assemblage,
inducinga completebreakdownto a mixtureof oxidesand
metallicalloys(Fe, FeSi). Thoughspeculative,a metal-oxide
layermay be heterogeneous
on manylengthscalesbecauseof
the disparatephysicalpropertiesof the two components
[see
also Knittle and Jean!oz, 1991]. This providesa possible
explanationfor observedheterogeneity
in D" on lengthscales
rangingfrom the smallestobservable
with seismicprobes(100
km, the size of a seismicwave) to nearlythe diameterof the
coreILarely et al., 1986; YoungandLay, 1987].
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andhightemperature,
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We thankC. Lithgow-Bertelloni,R.J.
Hemley and the refereesfor helpfulcomments.This work
supported
by NSF GrantEAR-8816819.
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M.S.T.-Bukowinski,
Dept.
ofGeology
andGeophysics,
University
of California,
Berkeley,
CA 94720.
Lars Stixrude,Geophysical
Laboratory,5251 Broad
BranchRd.NW, Washington,
DC 20015.
(Received
February!4, 1992;
accepted
April 16, 1992.)